{"title":"带约束的模糊关系方程的求解","authors":"Xueyan Xu","doi":"10.26599/fie.2023.9270017","DOIUrl":null,"url":null,"abstract":"This paper studies the resolution of the max-min compositional fuzzy relation equation with the constraint of <inline-formula id=\"M1\"> <math id=\"mathml_M1\" display=\"inline\" overflow=\"scroll\"><munderover><mo movablelimits=\"false\">∑</mo><mrow class=\"MJX-TeXAtom-ORD\"><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow class=\"MJX-TeXAtom-ORD\"><mrow class=\"MJX-TeXAtom-ORD\"><msub><mi>x</mi><mi>i</mi></msub></mrow></mrow><mo>=</mo><mn>1</mn></math></inline-formula>. The solvability and the unique solvability of this constrained fuzzy relation equation are characterized. Furthermore, this paper presents a resolution of it and designs a corresponding tabular method. Finally, a numerical example is provided to illustrate the resolution procedure.","PeriodicalId":37623,"journal":{"name":"Fuzzy Information and Engineering","volume":"11 1","pages":"0"},"PeriodicalIF":1.3000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Resolution of Fuzzy Relation Equations with Constraints\",\"authors\":\"Xueyan Xu\",\"doi\":\"10.26599/fie.2023.9270017\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper studies the resolution of the max-min compositional fuzzy relation equation with the constraint of <inline-formula id=\\\"M1\\\"> <math id=\\\"mathml_M1\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><munderover><mo movablelimits=\\\"false\\\">∑</mo><mrow class=\\\"MJX-TeXAtom-ORD\\\"><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow class=\\\"MJX-TeXAtom-ORD\\\"><mrow class=\\\"MJX-TeXAtom-ORD\\\"><msub><mi>x</mi><mi>i</mi></msub></mrow></mrow><mo>=</mo><mn>1</mn></math></inline-formula>. The solvability and the unique solvability of this constrained fuzzy relation equation are characterized. Furthermore, this paper presents a resolution of it and designs a corresponding tabular method. Finally, a numerical example is provided to illustrate the resolution procedure.\",\"PeriodicalId\":37623,\"journal\":{\"name\":\"Fuzzy Information and Engineering\",\"volume\":\"11 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fuzzy Information and Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26599/fie.2023.9270017\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Information and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26599/fie.2023.9270017","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Resolution of Fuzzy Relation Equations with Constraints
This paper studies the resolution of the max-min compositional fuzzy relation equation with the constraint of . The solvability and the unique solvability of this constrained fuzzy relation equation are characterized. Furthermore, this paper presents a resolution of it and designs a corresponding tabular method. Finally, a numerical example is provided to illustrate the resolution procedure.
期刊介绍：
Fuzzy Information and Engineering—An International Journal wants to provide a unified communication platform for researchers in a wide area of topics from pure and applied mathematics, computer science, engineering, and other related fields. While also accepting fundamental work, the journal focuses on applications. Research papers, short communications, and reviews are welcome. Technical topics within the scope include: (1) Fuzzy Information a. Fuzzy information theory and information systems b. Fuzzy clustering and classification c. Fuzzy information processing d. Hardware and software co-design e. Fuzzy computer f. Fuzzy database and data mining g. Fuzzy image processing and pattern recognition h. Fuzzy information granulation i. Knowledge acquisition and representation in fuzzy information (2) Fuzzy Sets and Systems a. Fuzzy sets b. Fuzzy analysis c. Fuzzy topology and fuzzy mapping d. Fuzzy equation e. Fuzzy programming and optimal f. Fuzzy probability and statistic g. Fuzzy logic and algebra h. General systems i. Fuzzy socioeconomic system j. Fuzzy decision support system k. Fuzzy expert system (3) Soft Computing a. Soft computing theory and foundation b. Nerve cell algorithms c. Genetic algorithms d. Fuzzy approximation algorithms e. Computing with words and Quantum computation (4) Fuzzy Engineering a. Fuzzy control b. Fuzzy system engineering c. Fuzzy knowledge engineering d. Fuzzy management engineering e. Fuzzy design f. Fuzzy industrial engineering g. Fuzzy system modeling (5) Fuzzy Operations Research [...] (6) Artificial Intelligence [...] (7) Others [...]
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